The present invention relates to an acoustic beam resonator in which resonant acoustic beam modes are generated. Beam modes are so named because they are mathematically identical to the possible cross-sectional power levels of a laser beam, H. Kogelnik and T. Li, "Laser Beams and Resonators," Applied Optics, 5, 1,550 - 1,567 (Oct., 1966), or the so-called beam waveguide, G. Goubau and F. Schwering, "On the Guided Propagation of Electromagnetic Wave Beams," IRE Trans. on Antennas and Propagation, AP-9, 248 - 256 (May, 1961). The use of a Fabry-Perot structure as a laser resonator, along with its analogous relationship to the beam waveguide for transmission of very short wavelength microwave power, has provided the impetus for developing the electromagnetic theory of its operation. Measurements at microwave frequencies have often been used to verify the theory and analyze the effect of different parameters for a Fabry-Perot resonator.
A Fabry-Perot resonator is basically two mirrors positioned on a common axis and displaced from each other by a distance d. In systems with "large aperture," i.e., when the radial extent of the mirrors is large enough to reflect all but a negligible portion of beam energy, diffraction is neglected and a wave analysis the resonator is carried out as follows.
A component of electric field, u, satisfies the scalar wave equation EQU .DELTA..sup.2 u + k.sup.2 u = 0 Eq. 1
where k = (2.pi./.lambda.) is the propagation constant. Since energy is traveling back and forth in a primarily axial direction solutions of the form EQU u = .psi. (r, .theta., z)e.sup.-.sup.jkz (cylindrical coordinates)
Or Eq. 2 .psi. EQU u = - (x, y, z)e.sup.-.sup.jkz (cartesian coordinates)
are substituted into Equation 1 where e.sup.-.sup.jkz is a plane wave in the z direction and .psi. represents the difference between the beam in the cavity and a plane wave.
Although the theory of operation of Fabry-Perot resonator has received considerable attention for electromagnetic waves within both the optical and microwave frequencies, the generation of acoustic resonant beam modes in a Fabry-Perot type of structure has not previously been reported. Acoustic waves, of course, are longitudinal and not transverse as are electromagnetic waves.